Abstract
Dynamic plane stress of sheets composed of two orthogonal families of inextensible fibers, with infinitesimal elastic shearing stress response, is considered. The fibers through the tip of a propagating tear or crack carry finite forces. Fracture criteria that can be expressed in terms of these tip forces are discussed. In a particular example it is shown that the maximum energy release rate criterion leads to a circular crack trajectory, while the so-called critical force and critical stress criteria imply that the crack is L-shaped, like cracks or tears in real fibrous materials.
Résumé
On considère la dynamique des contraintes de plaques planes composées de deux familles orthogonales de fibres inextensibles et ayant une response elastique au cisaillement. Les fibres en fin d'allongement ou de fracture supportent des forces finies. Differentes possibilités de critères de fractures en terme de ces forces sont etudiés. Dans un exemple particulier on montre que le critère de liberation maximale d'energie conduit à une propagation de fracture circulaire, alors que le critère des forces et contraintes critiques conduit a une fracture en forme de L comme c'est le cas pour les materiaux reels constitués de fibres.
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Mannion, L.F., Pipkin, A.C. Dynamic fracture of idealized fiber-reinforced materials. J Elasticity 13, 395–409 (1983). https://doi.org/10.1007/BF00042518
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DOI: https://doi.org/10.1007/BF00042518